Complete analytical solution to the quantum Yukawa potential

Abstract

We present a complete analytical solution to the quantum problem of a particle in the Yukawa potential, using supersymmetry and a systematic expansion of the corresponding super-potentials. Results for the critical screening of the ground state improve in several figures existing results based on both numerical solutions and approximation methods. Our calculation to order $(a_{0}/D)^{2}$ for the squared ground state wavefunction at the origin, which enter in darkonium transitions, yields a correction of $\pi^{4}/216$ to results based on variational techniques.